Accumulate shared product sums before dirty-anchor fanout

[1337isnot1337]

Result

This package extends the one-common-product dirty-anchor schedule to a shared sum of s >= 2 bilinear products. A required output accumulator with arbitrary dirty entry first compensates every other output for its old value, accumulates the entire common sum, and then broadcasts the updated anchor once. Each output receives the common sum plus its private product; reversing the schedule restores every arbitrary dirty accumulator.

For q outputs, direct evaluation uses q(s+1) product children. The anchor schedule uses s+q children and charges 2(q-1) width-w row additions. Repeating the one-term dirty-anchor fanout separately for each common product uses 2s(q-1) row additions, so the aggregate schedule saves 2(s-1)(q-1) additions. For q=s=3, this is 12 direct children versus 6 children plus 4 row additions; separate one-term fanout would use 12 row additions.

The local bill is exact. If mu is one child cost and A_w one width-w row-add cost, the net saving against independent evaluation is (q-1)(s*mu - 2*A_w). Eight hypothetical q=s=3 groups would change the rank-only fixed-word ceiling by only 0.905971%, even before adding the 32 width-one scalar additions, and the selected trace does not establish that placement. No supplier or kappa claim is made.

Verification

• python3 scripts/research_package.py --package research/recursive-multiterm-anchor-seedb9a23 --check-only
• python3.12 scripts/research_package.py --package research/recursive-multiterm-anchor-seedb9a23
• git diff --check

The package symbolically checks forward/inverse maps for 2 <= q <= 5, 1 <= s <= 4, exhausts all 60,073 q=s=2 dirty/input states over F2 and F3, and tests both missing-wave and wrong-sign failures.

Scope and overlap

This is a finite local construction. PR #1944 and active claim #18925817 cover s=1; this package changes the object to a shared multi-term sum and coalesces compensation across all common terms. PR #1907 uses a clean output anchor, PR #1872 uses a clean helper and cleanup, and PR #1155 treats generic linear restoration coalescing. Finding a source-incidence match in an admitted supplier remains open.

The work used substantial OpenAI Codex assistance. Selected-word construction credit remains with its original authors.

[Mister-Meeseeks]

Batch review at f039d4df1d2fa094771977fbe3584a9ba1149e86.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Arbitrary-dirty output anchor accumulates several shared products before two-wave fanout, saving source-preserving multiply-add calls and redundant compensation. Polynomial/inverse and F2/F3 state checks support the stated local contract. Hypothetical selected-profile placement is explicitly unconstructed; no supplier or frontier improvement.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.